Q. If $\int_{}^{}{\frac{dx}{x^{2} + 2x + 2} = f(x) + c}$, then $f(x)$ is equal to
A) $\tan^{- 1}{(x + 1)}$
B) $2\tan^{- 1}{(x + 1)}$
C) $- \tan^{- 1}{(x + 1)}$
D) $3\tan^{- 1}{(x + 1)}$
Explanation
(a)
Let $I = \int_{}^{}\frac{dx}{x^{2} + 2x + 2} = \int_{}^{}\frac{dx}{1 + (x + 1)^{2}}$
$= tan^{- 1}(x + 1) + c = f(x) + c$ [given]
$\therefore\ f(x) = \tan^{- 1}{(x + 1)}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.